Nested Regression Based Optimal Selection (NRBOS) of Rational Polynomial Coefficients

2014 ◽  
Vol 80 (3) ◽  
pp. 261-269 ◽  
Author(s):  
Long Tengfei ◽  
Jiao Weili ◽  
He Guojin
Keyword(s):  
Optimal Selection ◽  
Polynomial Coefficients ◽  
Rational Polynomial ◽  
Nested Regression

Evaluation of the RPC Model for Ziyuan-3 Three-Line Array Imagery

2017 ◽  
Author(s):  
Zhonghua Hong ◽  
Shengyuan Xu ◽  
Yun Zhang ◽  
Yanling Han ◽  
Yongjiu Feng
Keyword(s):  
Imaging System ◽  
Three Dimensional ◽  
Generic Model ◽  
Axis Direction ◽  
Polynomial Coefficients ◽  
Sensor Model ◽  
Rational Polynomial ◽  
Line Array ◽  
Physical Sensor ◽  
Sensor Models

Ziyuan-3 (ZY-3) satellite is the first civilian stereo mapping satellite in China and was designed to achieve the 1: 50000 scale mapping for land and ocean. Rigorous sensor model (RSM) is required to build the relationship between the three-dimensional (3D) object space and two-dimensional (2D) image space of ZY-3 satellite imagery. However, each satellite sensor has its own imaging system with different physical sensor models, which increase the difficulty of geometric integration of multi-source images with different sensor models. Therefore, it is critical to generate generic model especially rational polynomial coefficients (RPCs) of optical imagery. Recently, relatively a few researches have been conducted on RPCs generation to ZY-3 satellite. This paper proposes an approach to evaluate the performance of RPCs generation from RSM of ZY-3 imagery. Three scenarios experiments with different terrain features (such as ocean, city and grassland) are designed and conducted to comprehensively evaluate the replacement accuracies of this approach and analyze the RPCs fitting error. All the experimental results demonstrate that the proposed method achieved encouraging accuracy of better than 1.946E-04 pixel in both x-axis direction and y-axis direction, it indicates that the RPCs is suitable for ZY-3 imagery and can be used as a replacement for the RSM of ZY-3 imagery.

scholarly journals PROBLEMS AND LIMITATIONS OF SATELLITE IMAGE ORIENTATION FOR DETERMINATION OF HEIGHT MODELS

2017 ◽  
Vol XLII-1/W1 ◽  
pp. 257-264 ◽  
Author(s):  
K. Jacobsen
Keyword(s):  
Bias Correction ◽  
Satellite Image ◽  
Surface Model ◽  
Negative Effects ◽  
3 Dimensional ◽  
Polynomial Coefficients ◽  
Rational Polynomial ◽  
Sensor Orientation ◽  
Image Orientation ◽  
Linear Trends

The usual satellite image orientation is based on bias corrected rational polynomial coefficients (RPC). The RPC are describing the direct sensor orientation of the satellite images. The locations of the projection centres today are without problems, but an accuracy limit is caused by the attitudes. Very high resolution satellites today are very agile, able to change the pointed area over 200km within 10 to 11 seconds. The corresponding fast attitude acceleration of the satellite may cause a jitter which cannot be expressed by the third order RPC, even if it is recorded by the gyros. Only a correction of the image geometry may help, but usually this will not be done. The first indication of jitter problems is shown by systematic errors of the y-parallaxes (py) for the intersection of corresponding points during the computation of ground coordinates. These y-parallaxes have a limited influence to the ground coordinates, but similar problems can be expected for the x-parallaxes, determining directly the object height. Systematic y-parallaxes are shown for Ziyuan-3 (ZY3), WorldView-2 (WV2), Pleiades, Cartosat-1, IKONOS and GeoEye. Some of them have clear jitter effects. In addition linear trends of py can be seen. Linear trends in py and tilts in of computed height models may be caused by limited accuracy of the attitude registration, but also by bias correction with affinity transformation. The bias correction is based on ground control points (GCPs). The accuracy of the GCPs usually does not cause some limitations but the identification of the GCPs in the images may be difficult. With 2-dimensional bias corrected RPC-orientation by affinity transformation tilts of the generated height models may be caused, but due to large affine image deformations some satellites, as Cartosat-1, have to be handled with bias correction by affinity transformation. Instead of a 2-dimensional RPC-orientation also a 3-dimensional orientation is possible, respecting the object height more as by 2-dimensional orientation. The 3-dimensional orientation showed advantages for orientation based on a limited number of GCPs, but in case of poor GCP distribution it may cause also negative effects. For some of the used satellites the bias correction by affinity transformation showed advantages, but for some other the bias correction by shift was leading to a better levelling of the generated height models, even if the root mean square (RMS) differences at the GCPs were larger as for bias correction by affinity transformation. <br><br> The generated height models can be analyzed and corrected with reference height models. For the used data sets accurate reference height models are available, but an analysis and correction with the free of charge available SRTM digital surface model (DSM) or ALOS World 3D (AW3D30) is also possible and leads to similar results. The comparison of the generated height models with the reference DSM shows some height undulations, but the major accuracy influence is caused by tilts of the height models. Some height model undulations reach up to 50&amp;thinsp;% of the ground sampling distance (GSD), this is not negligible but it cannot be seen not so much at the standard deviations of the height. In any case an improvement of the generated height models is possible with reference height models. If such corrections are applied it compensates possible negative effects of the type of bias correction or 2-dimensional orientations against 3-dimensional handling.

Application of 30-meter global digital elevation models for compensating rational polynomial coefficients biases

2019 ◽  
Vol 35 (12) ◽  
pp. 1311-1326 ◽  
Author(s):  
Amin Alizadeh Naeini ◽  
Sayyed Bagher Fatemi ◽  
Masoud Babadi ◽  
Sayyed Mohammad Javad Mirzadeh ◽  
Saeid Homayouni
Keyword(s):  
Digital Elevation Models ◽  
Polynomial Coefficients ◽  
Rational Polynomial ◽  
Digital Elevation

Rational polynomial windows with high attenuation of sidelobes

2012 ◽  
Vol 61 (1) ◽  
pp. 7-14
Author(s):  
Krzysztof Okarma
Keyword(s):  
Computational Complexity ◽  
Frequency Characteristics ◽  
Low Computational Complexity ◽  
High Attenuation ◽  
Low Level ◽  
Polynomial Coefficients ◽  
Rational Polynomial ◽  
Division Operation

Rational polynomial windows with high attenuation of sidelobes In the paper the idea of rational polynomial windows optimised towards low level of Fourier spectrum's sidelobes is presented. A relevant advantage of the polynomial windows family and their modifications is their ability to easily change their properties changing only the values of the polynomial coefficients. The obtained frequency characteristics demonstrate better properties of proposed rational windows than their standard polynomial equivalents requiring only the additional division operation. Such approach does not increase the computational complexity in significant way and the great advantage of polynomial windows which is their low computational complexity is preserved.

scholarly journals RPC-Based Orthorectification for Satellite Images Using FPGA

Sensors ◽  
2018 ◽  
Vol 18 (8) ◽  
pp. 2511 ◽  
Author(s):  
Rongting Zhang ◽  
Guoqing Zhou ◽  
Guangyun Zhang ◽  
Xiang Zhou ◽  
Jingjin Huang
Keyword(s):  
Fixed Point ◽  
Processing Speed ◽  
Satellite Images ◽  
Polynomial Coefficients ◽  
Rational Polynomial ◽  
Field Programmable ◽  
Fpga Chip ◽  
Mean Square Errors ◽  
Point Arithmetic ◽  
Speed And Accuracy

Conventional rational polynomial coefficients (RPC)-based orthorectification methods are unable to satisfy the demands of timely responses to terrorist attacks and disaster rescue. To accelerate the orthorectification processing speed, we propose an on-board orthorectification method, i.e., a field-programmable gate array (FPGA)-based fixed-point (FP)-RPC orthorectification method. The proposed RPC algorithm is first modified using fixed-point arithmetic. Then, the FP-RPC algorithm is implemented using an FPGA chip. The proposed method is divided into three main modules: a reading parameters module, a coordinate transformation module, and an interpolation module. Two datasets are applied to validate the processing speed and accuracy that are achievable. Compared to the RPC method implemented using Matlab on a personal computer, the throughputs from the proposed method and the Matlab-based RPC method are 675.67 Mpixels/s and 61,070.24 pixels/s, respectively. This means that the proposed method is approximately 11,000 times faster than the Matlab-based RPC method to process the same satellite images. Moreover, the root-mean-square errors (RMSEs) of the row coordinate (ΔI), column coordinate (ΔJ), and the distance ΔS are 0.35 pixels, 0.30 pixels, and 0.46 pixels, respectively, for the first study area; and, for the second study area, they are 0.27 pixels, 0.36 pixels, and 0.44 pixels, respectively, which satisfies the correction accuracy requirements in practice.

scholarly journals Refining IKONOS DEM for Dehradun Region Using Photogrammetry Based DEM Editing Methods, Orthoimage Generation and Quality Assessment of Cartosat-1 DEM

2020 ◽  
Vol 5 (1) ◽  
pp. 3
Author(s):  
Ashutosh Bhardwaj ◽  
Kamal Jain ◽  
Rajat Subhra Chatterjee
Keyword(s):  
High Resolution ◽  
Large Scale ◽  
Digital Terrain Model ◽  
Optimal Number ◽  
Mean Difference ◽  
Surface Model ◽  
Difference Image ◽  
Polynomial Coefficients ◽  
Rational Polynomial ◽  
The Difference

The correct representation of the topography of terrain is an important requirement to generate photogrammetric products such as orthoimages and maps from high-resolution (HR) or very high-resolution (VHR) satellite datasets. The refining of the digital elevation model (DEM) for the generation of an orthoimage is a vital step with a direct effect on the final accuracy achieved in the orthoimages. The refined DEM has potential applications in various domains of earth sciences such as geomorphological analysis, flood inundation mapping, hydrological analysis, large-scale mapping in an urban environment, etc., impacting the resulting output accuracy. Manual editing is done in the presented study for the automatically generated DEM from IKONOS data consequent to the satellite triangulation with a root mean square error (RMSE) of 0.46, using the rational function model (RFM) and an optimal number of ground control points (GCPs). The RFM includes the rational polynomial coefficients (RPCs) to build the relation between image space and ground space. The automatically generated DEM initially represents the digital surface model (DSM), which is used to generate a digital terrain model (DTM) in this study for improving orthoimages for an area of approximately 100 km2. DSM frequently has errors due to mass points in hanging (floating) or digging, which need correction while generating DTM. The DTM assists in the removal of the geometric effects (errors) of ground relief present in the DEM (i.e., DSM here) while generating the orthoimages and thus improves the quality of orthoimages, especially in areas such as Dehradun that have highly undulating terrain with a large number of natural drainages. The difference image of reference, i.e., edited IKONOS DEM (now representing DTM) and automatically generated IKONOS DEM, i.e., DSM, has a mean difference of 1.421 m. The difference DEM (dDEM) for the reference IKONOS DEM and generated Cartosat-1 DEM at a 10 m posting interval (referred to as Carto10 DEM) results in a mean difference of 8.74 m.

scholarly journals GEOMETRIC STITCHING METHOD FOR DOUBLE CAMERAS WITH WEAK CONVERGENCE GEOMETRY

2017 ◽  
Vol XLII-1/W1 ◽  
pp. 71-74
Author(s):  
N. Zhou ◽  
H. He ◽  
Y. Bao ◽  
C. Yue ◽  
K. Xing ◽  
...  
Keyword(s):  
Weak Convergence ◽  
Relative Orientation ◽  
Test Results ◽  
Polynomial Coefficients ◽  
Aster Gdem ◽  
Rational Polynomial ◽  
Digital Elevation ◽  
Transform Coefficients ◽  
Elevation Model ◽  
Orientation Parameters

In this paper, a new geometric stitching method is proposed which utilizes digital elevation model (DEM)-aided block adjustment to solve relative orientation parameters for dual-camera with weak convergence geometry. A rational function model (RFM) with affine transformation is chosen as the relative orientation model. To deal with the weak geometry, a reference DEM is used in this method as an additional constraint in the block adjustment, which only calculates the planimetry coordinates of tie points (TPs). After that we can use the obtained affine transform coefficients to generate virtual grid, and update rational polynomial coefficients (RPCs) to complete the geometric stitching. Our proposed method was tested on GaoFen-2(GF-2) dual-camera panchromatic (PAN) images. The test results show that the proposed method can achieve an accuracy of better than 0.5 pixel in planimetry and have a seamless visual effect. For regions with small relief, when global DEM with 1&amp;thinsp;km grid, SRTM with 90&amp;thinsp;m grid and ASTER GDEM V2 with 30&amp;thinsp;m grid replaced DEM with 1m grid as elevation constraint， it is almost no loss of accuracy. The test results proved the effectiveness and feasibility of the stitching method.

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